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- Michael Molloy, Bruce A. Reed
- Random Struct. Algorithms
- 1995

Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n ver-tices of degree i. Essentially, we show that if P i(i?2) i > 0 then such graphs almost surely have a giant component, while if P i(i?2) i < 0 then almost surely all components in such graphs are small. We can apply these results… (More)

- Michael Molloy, Bruce A. Reed
- Combinatorics, Probability & Computing
- 1998

Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider a random graph having approximately i n ver-tices of degree i. In 12] the authors essentially show that if P i(i ? 2) i > 0 then the graph a.s. has a giant component, while if P i(i ? 2) i < 0 then a.s. all components in the graph are small. In this paper we analyze the… (More)

- Michael Molloy, Bruce A. Reed
- J. Comb. Theory, Ser. B
- 1997

Recently there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Rather intriguingly, experimental results with various models for generating random CSP instances suggest a \threshold-like" behavior and some theoretical work has been done in analyzing these models when… (More)

- Michael Molloy, Mohammad R. Salavatipour
- J. Comb. Theory, Ser. B
- 2005

- Michael Molloy
- Random Struct. Algorithms
- 2005

- Michael Molloy, Bruce A. Reed
- STOC
- 1998

We provide a met.hod to produce an efficient algorithm to find an object whose existence is guaranteed by the Lo&z Local Lemma. We feel that this method will apply to the vast. majority of applications of the Local Lemma, unless t,he application has one of four problematic traits. However, proving that the method applies to a particular application may… (More)

- Alan M. Frieze, Mark Jerrum, Michael Molloy, Robert W. Robinson, Nicholas C. Wormald
- J. Algorithms
- 1996

- Michael Molloy
- SIAM J. Comput.
- 2003

We introduce a class of models for random Constraint Satisfaction Problems. This class includes and generalizes many previously studied models. We characterize those models from our class which are asymptot-ically interesting in the sense that the limiting probability of satissability changes signiicantly as the number of constraints increases. We also… (More)

- Michael Molloy
- SIAM J. Comput.
- 2004